Hydrodynamic forces in water exit problems

Abstract

The three-dimensional steady problem of an elongated smooth body moving along the water free surface at a constant speed is considered within the 2D+T approximation. The corresponding unsteady two-dimensional problem describes both the water entry and the subsequent exit of a smooth contour from the water. The shape of the contour varies in time. The present paper is concerned with the exit stage. The draft of the body is small compared with the body length and beam. The hydrodynamic loads during the entry stage are evaluated by the original Wagner model of water impact. The linearized exit model [5] is generalised to account for time-dependent acceleration of the body and the body shape which also varies in time. The integral equation with respect to the size of the wetted area of the body is solved numerically. The theoretical predictions of the hydrodynamic forces acting on the body during its exit from the liquid are compared with the numerical results obtained by solving the Navier-Stokes equations. A simplified model of water exit with the body shape approximated by a parabolic contour with a time-dependent radius of curvature is proposed and validated. It is shown that the linearized water-exit model with non-linear correction terms predicts reasonably well the hydrodynamic loads.

Hydroelastic effects during the fast lifting of a disc from a water surface

“…Although at very short times this approach yields reasonable results, as was shown for instance by the numerical simulations of Korobkin et al (2017a) as well as by our experimental observations (see figure 4b), eventually the acceleration predicted by the theory significantly departs from the acceleration at the center of the plate obtained experimentally. Most notably, the observed accelerations even decrease in response to a monotonically increasing force.…”

“…The linearised model of two-dimensional water exit was generalised, and validated using CFD results, by Korobkin et al (2017a) to include arbitrary motions of bodies and bodies of time-varying shapes. The model was developed further to be included in the two-dimensions-plus-time analysis of aircraft ditching.…”

Experimental investigation of the water entry and/or exit of axisymmetric bodies

“…These observations lead us to the important conclusion that a similar water exit model can be used to model both a pure water exit event and the exit stage of a combined water entry and exit event (e.g. in a 2D + t approach such as the one used in Bensch et al (2001), see also Tassin et al (2013) and Korobkin et al (2017a)).…”

“…In the linearized water exit model proposed by Korobkin (2013), and further developed in Korobkin et al (2017a), the body shape has no effect on the evolution of the wetted surface, provided that the size of the initial wetted surface and the body motion are similar. In order to confirm experimentally this assumption, we compare the results obtained with the different body shapes (circular disc, cone, sphere), but with a similar value of c 0 and Figure 32 shows the evolution of the radius of the wetted surface as a function of the elevation h(t) measured during the water exit of the three mock-ups for c 0 = 200 mm.…”

“…(iii) The evolution of the wetted surface measured during a water exit experiment is compared with the evolution of the wetted surface measured during the exit stage of a combined water entry and exit experiment. (iv) The experimental results are compared with different theoretical models: the combined Wagner-modified von Karman model of Tassin et al (2013), the linearized water exit model of Korobkin, Khabakhpasheva & Maki (2017a) and the small-time self-similar solution of Korobkin, Khabakhpasheva & Rodríguez-Rodríguez (2017b). For this purpose, an extension of the linearized model of Korobkin et al (2017a) to the water exit of a rigid axisymmetric body with an arbitrary exit kinematics (ḧ(t) ≥ 0) was implemented.…”